Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Tricorns and Multicorns of -Iteration Scheme Wed, 28 Jan 2015 12:03:57 +0000 http://www.hindawi.com/journals/jfs/2015/417167/ Complex graphics of dynamical system have striking features of fractals and become a wide area of research due to their beauty and complexity of their nature. The aim of this paper is to study dynamics of relative superior tricorns and multicorns using -iteration schemes. Several examples are presented to explore the geometry of relative superior tricorns and multicorns for antipolynomial of complex polynomial for . Shin Min Kang, Arif Rafiq, Abdul Latif, Abdul Aziz Shahid, and Young Chel Kwun Copyright © 2015 Shin Min Kang et al. All rights reserved. Nontrivial Solutions for Periodic Schrödinger Equations with Sign-Changing Nonlinearities Thu, 15 Jan 2015 14:02:06 +0000 http://www.hindawi.com/journals/jfs/2015/757153/ We prove a new infinite-dimensional linking theorem. Using this theorem, we obtain nontrivial solutions for strongly indefinite periodic Schrödinger equations with sign-changing nonlinearities. Shaowei Chen, Lishan Lin, and Liqin Xiao Copyright © 2015 Shaowei Chen et al. All rights reserved. Boundedness of Marcinkiewicz Integrals and Their Commutators on Generalized Weighted Morrey Spaces Thu, 15 Jan 2015 11:05:31 +0000 http://www.hindawi.com/journals/jfs/2015/450145/ We will study the boundedness of Marcinkiewicz integrals with rough kernel on the generalized weighted Morrey spaces. We will also prove that the commutator operators formed by a function and Marcinkiewicz integrals are also bounded on the generalized weighted Morrey spaces. Runqing Cui and Zhang Li Copyright © 2015 Runqing Cui and Zhang Li. All rights reserved. Uniform Extendibility of the Bergman Kernel for Generalized Minimal Balls Wed, 14 Jan 2015 14:04:06 +0000 http://www.hindawi.com/journals/jfs/2015/919465/ We consider a class of convex domains which contains non-Reinhardt domains with nonsmooth boundary. We show that the domains of this class satisfy the condition Q. Jong-Do Park Copyright © 2015 Jong-Do Park. All rights reserved. Caristi Type Selections of Multivalued Mappings Sun, 11 Jan 2015 07:18:07 +0000 http://www.hindawi.com/journals/jfs/2015/941856/ Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems. Calogero Vetro and Francesca Vetro Copyright © 2015 Calogero Vetro and Francesca Vetro. All rights reserved. Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation Tue, 06 Jan 2015 08:06:58 +0000 http://www.hindawi.com/journals/jfs/2015/213679/ For a Banach space and a measure space , let be the space of all -valued countably additive measures on of bounded variation, with the total variation norm. In this paper we give a characterization of weakly precompact subsets of . Ioana Ghenciu Copyright © 2015 Ioana Ghenciu. All rights reserved. Two-Weight Extrapolation on Lorentz Spaces Thu, 01 Jan 2015 09:33:34 +0000 http://www.hindawi.com/journals/jfs/2015/182921/ We give several two-weight extrapolation theorems on Lorentz spaces which extend the results of Cruz-Uribe and Pérez (2000) and some applications for the singular integral operators, the potential type operators, and commutators. Wenming Li, Tingting Zhang, and Limei Xue Copyright © 2015 Wenming Li et al. All rights reserved. A Note on the Generalized Camassa-Holm Equation Thu, 25 Dec 2014 12:59:25 +0000 http://www.hindawi.com/journals/jfs/2014/975925/ We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked solutions and apply them to prove the ill-posedness in with . Yun Wu and Ping Zhao Copyright © 2014 Yun Wu and Ping Zhao. All rights reserved. Global Existence and Blow-Up for the Euler-Bernoulli Plate Equation with Variable Coefficients Thu, 25 Dec 2014 00:10:16 +0000 http://www.hindawi.com/journals/jfs/2014/176429/ We prove the local existence, blow-up, global existence, and stability of solutions to the initial boundary value problem for Euler-Bernoulli plate equation with variable coefficients. Jianghao Hao and Jie Lan Copyright © 2014 Jianghao Hao and Jie Lan. All rights reserved. Some Topological Properties of Mon, 22 Dec 2014 00:10:16 +0000 http://www.hindawi.com/journals/jfs/2014/195262/ If is a completely regular space, first we characterize those spaces whose compact sets are metrizable. Then we use this result to provide a general condition for to ensure the metrizability of compact sets in . Finally, we characterize those spaces that have a -basis. Juan Carlos Ferrando Copyright © 2014 Juan Carlos Ferrando. All rights reserved. Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces Mon, 08 Dec 2014 12:22:45 +0000 http://www.hindawi.com/journals/jfs/2014/720875/ We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness of these operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces. Xiao Jin Zhang and Xian Ming Hou Copyright © 2014 Xiao Jin Zhang and Xian Ming Hou. All rights reserved. Weak Compactness of Almost Limited Operators Wed, 03 Dec 2014 00:10:17 +0000 http://www.hindawi.com/journals/jfs/2014/263159/ This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if is a -Dedekind complete Banach lattice, then every almost limited operator is weakly compact if and only if is reflexive or the norm of is order continuous. Also, we show that if is a -Dedekind complete Banach lattice, then the square of every positive almost limited operator is weakly compact if and only if the norm of is order continuous. Aziz Elbour, Nabil Machrafi, and Mohammed Moussa Copyright © 2014 Aziz Elbour et al. All rights reserved. Generalized Composition Operators on Zygmund-Orlicz Type Spaces and Bloch-Orlicz Type Spaces Sun, 30 Nov 2014 07:56:56 +0000 http://www.hindawi.com/journals/jfs/2014/549370/ The boundedness and compactness of generalized composition operators on Zygmund-Orlicz type spaces and Bloch-Orlicz type spaces are established in this paper. Congli Yang, Fangwei Chen, and Pengcheng Wu Copyright © 2014 Congli Yang et al. All rights reserved. Higher Order Sobolev-Type Spaces on the Real Line Tue, 25 Nov 2014 12:26:45 +0000 http://www.hindawi.com/journals/jfs/2014/261565/ This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces. Bogdan Bojarski, Juha Kinnunen, and Thomas Zürcher Copyright © 2014 Bogdan Bojarski et al. All rights reserved. Approximate Generalized Cubic -Derivations Thu, 20 Nov 2014 13:38:34 +0000 http://www.hindawi.com/journals/jfs/2014/757956/ We will show the general solution of the functional equation = and investigate the stability of cubic -derivations associated with the given functional equation on Banach -algebras. Heejeong Koh and Dongseung Kang Copyright © 2014 Heejeong Koh and Dongseung Kang. All rights reserved. Blowup of Solution for a Class of Doubly Nonlinear Parabolic Systems Tue, 18 Nov 2014 06:36:38 +0000 http://www.hindawi.com/journals/jfs/2014/924596/ An initial boundary value problem for a class of doubly parabolic equations is studied. We obtain sufficient conditions for the blowup of solutions under suitable initial data using differential inequalities. Jun Lu, Qingying Hu, and Hongwei Zhang Copyright © 2014 Jun Lu et al. All rights reserved. Existence of Nontrivial Solutions for a Critical Perturbed Quasilinear Elliptic System Mon, 17 Nov 2014 06:50:27 +0000 http://www.hindawi.com/journals/jfs/2014/758963/ We consider a perturbed quasilinear elliptic system involving the -Laplacian with critical growth terms in . Under proper conditions, we establish the existence of nontrivial solutions by using the variational methods. Huixing Zhang and Xiangzhi Zhang Copyright © 2014 Huixing Zhang and Xiangzhi Zhang. All rights reserved. On the Compactness of the Commutator of the Parabolic Marcinkiewicz Integral with Variable Kernel Wed, 12 Nov 2014 11:48:56 +0000 http://www.hindawi.com/journals/jfs/2014/693534/ The authors prove that the commutator of the parabolic Marcinkiewicz integral with variable kernel is a compact operator on if and only if . The result is substantial improvement and extension of some known results. Yanping Chen, Kai Zhu, and Yong Ding Copyright © 2014 Yanping Chen et al. All rights reserved. On Continuity of Functions between Vector Metric Spaces Wed, 12 Nov 2014 08:17:27 +0000 http://www.hindawi.com/journals/jfs/2014/753969/ We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems. Cüneyt Çevik Copyright © 2014 Cüneyt Çevik. All rights reserved. On Isometric Extension in the Space Tue, 21 Oct 2014 07:54:45 +0000 http://www.hindawi.com/journals/jfs/2014/678407/ We study the problem of isometric extension on a sphere of the space . We give an affirmative answer to Tingley’s problem in the space . Xiaohong Fu Copyright © 2014 Xiaohong Fu. All rights reserved. Marcinkiewicz Integral Operators and Commutators on Herz Spaces with Variable Exponents Wed, 15 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/430365/ Our aim in this paper is to give the boundedness of the Marcinkiewicz integral on Herz spaces and , where the two main indices are variable. Meanwhile, we consider the boundedness of the higher order commutator generated by and a function in BMO on these spaces. Liwei Wang Copyright © 2014 Liwei Wang. All rights reserved. Positive Solutions of a Kind of Equations Related to the Laplacian and -Laplacian Tue, 14 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/364010/ Positive solutions of a kind of equations related to the Laplacian and -Laplacian on a bounded domain in with are studied by using variational method. A sufficient condition of the existence of positive solutions is characterized by the eigenvalues of linear and another nonlinear eigenvalue problems. Fangfang Zhang and Zhanping Liang Copyright © 2014 Fangfang Zhang and Zhanping Liang. All rights reserved. Dual Algebras and A-Measures Mon, 13 Oct 2014 14:23:00 +0000 http://www.hindawi.com/journals/jfs/2014/364271/ Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphy , our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity of . We also investigate the relation between the algebra of bounded holomorphic functions on and its abstract counterpart—the * closure of a function algebra A in the dual of the band of measures generated by one of Gleason parts of the spectrum of A. Marek Kosiek and Krzysztof Rudol Copyright © 2014 Marek Kosiek and Krzysztof Rudol. All rights reserved. A Unified Approach to Some Classes of Nonlinear Integral Equations Wed, 03 Sep 2014 10:37:32 +0000 http://www.hindawi.com/journals/jfs/2014/306231/ We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed. Nurgali K. Ashirbayev, Józef Banaś, and Raina Bekmoldayeva Copyright © 2014 Nurgali K. Ashirbayev et al. All rights reserved. Ulam’s Type Stability and Fixed Points Methods Wed, 03 Sep 2014 09:08:23 +0000 http://www.hindawi.com/journals/jfs/2014/465861/ Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, Zbigniew Leśniak, and Bing Xu Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Locally Lipschitz Composition Operators in Space of the Functions of Bounded -Variation Mon, 01 Sep 2014 07:35:09 +0000 http://www.hindawi.com/journals/jfs/2014/606307/ We give a necessary and sufficient condition on a function under which the nonlinear composition operator , associated with the function , , acts in the space and satisfies a local Lipschitz condition. Odalis Mejía, Nelson José Merentes Díaz, and Beata Rzepka Copyright © 2014 Odalis Mejía et al. All rights reserved. A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points Thu, 28 Aug 2014 11:49:42 +0000 http://www.hindawi.com/journals/jfs/2014/675735/ Let be complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that is starshaped where . For every point , define : y lies on some geodesic segment in S from x to a point of kerS. There is a finite collection of all maximal sets whose union is S. Further, ker in . Adem Kılıcman and Wedad Saleh Copyright © 2014 Adem Kılıcman and Wedad Saleh. All rights reserved. Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations Wed, 27 Aug 2014 07:56:29 +0000 http://www.hindawi.com/journals/jfs/2014/246258/ We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained. Yuanhong Wei Copyright © 2014 Yuanhong Wei. All rights reserved. Spectral Distribution of Transport Operator Arising in Growing Cell Populations Mon, 25 Aug 2014 10:46:44 +0000 http://www.hindawi.com/journals/jfs/2014/748792/ Transport equation with partly smooth boundary conditions arising in growing cell populations is studied in space. It is to prove that the transport operator generates a semigroup and the ninth-order remainder term of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operator consists of only finite isolated eigenvalues with finite algebraic multiplicities in a trip . The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach. Hongxing Wu, Shenghua Wang, and Dengbin Yuan Copyright © 2014 Hongxing Wu et al. All rights reserved. The Boundedness of Marcinkiewicz Integrals Associated with Schrödinger Operator on Morrey Spaces Wed, 20 Aug 2014 11:10:55 +0000 http://www.hindawi.com/journals/jfs/2014/901267/ Let be a Schrödinger operator, where belongs to some reverse Hölder class. The authors establish the boundedness of Marcinkiewicz integrals associated with Schrödinger operators and their commutators on Morrey spaces. Dongxiang Chen and Fangting Jin Copyright © 2014 Dongxiang Chen and Fangting Jin. 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